On the degree of parallelism for parallel real-time tasks

The degree of parallelism, which measures how a task can execute concurrently, is an important characterization in scheduling. This paper studies the degree of parallelism in the domain of real-time scheduling of parallel tasks, including the DAG task model and the conditional DAG task model. The definition of the degree of parallelism for DAG tasks is clarified; the definition and computing algorithm of the degree of parallelism for conditional DAG tasks are proposed. By leveraging the degree of parallelism, new response time bounds are derived and simple but effective real-time scheduling approaches are presented. This research is the first work to study the degree of parallelism for conditional DAG tasks and explore its benefits in real-time scheduling. Experimental results demonstrate that the proposed scheduling approaches significantly outperform existing state-of-the-art methods.